You plan to cut a board into 3 pieces to repair part of a railing. You are going to cut the two ends of the board off into two equal pieces that are 1.1 feet long, if the remaining piece needs to be 2.30 times longer than the each of the first two cuts what length board should you buy? Round to the nearest tenth.

Answer:

semoga jawapan ini dapat membantu

Step-by-step explanation:

The Graph of a Quadratic Function

A quadratic function is a polynomial function of degree 2 which can be written in the general form,

f(x)=ax2+bx+c

Here a, b and c represent real numbers where a≠0. The squaring function f(x)=x2 is a quadratic function whose graph follows.

This general curved shape is called a parabola and is shared by the graphs of all quadratic functions. Note that the graph is indeed a function as it passes the vertical line test. Furthermore, the domain of this function consists of the set of all real numbers (−∞,∞) and the range consists of the set of nonnegative numbers [0,∞).

When graphing parabolas, we want to include certain special points in the graph. The y-intercept is the point where the graph intersects the y-axis. The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of the graph. Lastly, the line of symmetry (also called the axis of symmetry) is the vertical line through the vertex, about which the parabola is symmetric.

For any parabola, we will find the vertex and y-intercept. In addition, if the x-intercepts exist, then we will want to determine those as well. Guessing at the x-values of these special points is not practical; therefore, we will develop techniques that will facilitate finding them. Many of these techniques will be used extensively as we progress in our study of algebra.

Given a quadratic function f(x)=ax2+bx+c, find the y-intercept by evaluating the function where x=0. In general, f(0)=a(0)2+b(0)+c=c, and we have

y-intercept       (0,c)

Next, recall that the x-intercepts, if they exist, can be found by setting f(x)=0. Doing this, we have a2+bx+c=0, which has general solutions given by the quadratic formula, x=

−b±

√

b2−4ac

2a

. Therefore, the x-intercepts have this general form:

x-intercepts (

−b−

√

b2−4ac

2a

,0)    and    (

−b+

√

b2−4ac

2a

,0) 

Using the fact that a parabola is symmetric, we can determine the vertical line of symmetry using the x-intercepts. To do this, we find the x-value midway between the x-intercepts by taking an average as follows:

x = (

−b−

√

b2−4ac

2a

+

−b+

√

b2−4ac

2a

) ÷2 = (

−b−

√

b2−4ac

−b+

√

b2−4ac

2a

)÷(

2

1

) =

−2b

2a

⋅

1

2

= −

b

2a

Therefore, the line of symmetry is the vertical line x=−

b

2a

. We can use the line of symmetry to find the the vertex.

Line of symmetry Vertex x=−

b

2a

(−

b

2a

,f(−

b

2a

))

Generally three points determine a parabola. However, in this section we will find five points so that we can get a better approximation of the general shape. The steps for graphing a parabola are outlined in the following example.

Example 1

Graph: f(x)=−x2−2x+3.

Solution:

Step 1: Determine the y-intercept. To do this, set x=0 and find f(0).

f(x) = −x2−2x+3 f(0) = −(0)2−2(0)+3 = 3

The y-intercept is (0,3).

Step 2: Determine the x-intercepts if any. To do this, set f(x)=0 and solve for x.

f(x) = −x2−2x+3 Set f(x)=0. 0 = −x2−2x+3 Multiply both sides by −1. 0 = x2+2x−3 Factor. 0 = (x+3)(x−1) Set each factor equal to zero. x+3 = 0 or x−1 = 0 x = −3 x = 1

Here where f(x)=0, we obtain two solutions. Hence, there are two x-intercepts, (−3,0) and (1,0).

Step 3: Determine the vertex. One way to do this is to first use x=−

b

2a

to find the x-value of the vertex and then substitute this value in the function to find the corresponding y-value. In this example, a=−1 and b=−2.

x =

−b

2a

=

−(−2)

2(−1)

=

2

−2

= −1

Substitute −1 into the original function to find the corresponding y-value.

f(x) = −x2−2x+3 f(−1) = −(−1)2−2(−1)+3 = −1+2+3 = 4

The vertex is (−1,4).

Step 4: Determine extra points so that we have at least five points to plot. Ensure a good sampling on either side of the line of symmetry. In this example, one other point will suffice. Choose x=−2 and find the corresponding y-value.

x   y Point −2   3 f(−2)=−(−2)2−2(−2)+3=−4+4+3=3 (−2,3)

Our fifth point is (−2,3).

Step 5: Plot the points and sketch the graph. To recap, the points that we have found are

y-intercept: (0,3) x-intercepts: (−3,0) and (1,0) Vertex: (−1,4) Extra point: (−2,3)

Answer:

The parabola opens downward. In general, use the leading coefficient to determine if the parabola opens upward or downward. If the leading coefficient is negative, as in the previous example, then the parabola opens downward. If the leading coefficient is positive, then the parabola opens upward.

All quadratic functions of the form f(x)=ax2+bx+c have parabolic graphs with y-intercept (0,c). However, not all parabolas have x-intercepts.

Answer:

x = -4

Step-by-step explanation:

-2(3x - 4) - x - 3 = 33

~Simplify

-6x + 8 - x - 3

-7x + 5 = 33

~Subtract 3 to both sides

-7x = 28

~Divide -7 to both sides

x = -4

Best of Luck!

Answer:

x = -4

Step-by-step explanation:

-2(3x - 4) - x - 3 = 33

solve the brackets first

-6x + 8 -x -3 = 33

-6x - x + 8 - 3 = 33

-7x + 5 = 33

-7x = 33-5

-7x = 28

x = 28/ -7

x = -4

Answer:

Mean - 7.43

Median - 6

Mode - 8

Range - 13

Step-by-step explanation:

To find the mean/average, add up all the numbers and divide the sum by the # of data points.  (ex. you have 7 numbers, so you divide the sum of the numbers by 7.)

The median of a set of data is the middle number of ascending numbers in the data.  If there was an even number of data points you would have to add the 2 middle numbers and divide by 2.

The mode is the number that appears most frequently in the data set.

To find the range, just subtract the lowest number in the data set from the greatest number.

Answer:

mean= 7.4, median = 6, mode =6, range = 13

Step-by-step explanation:

mean = 10 + 15 + 5 + 8 + 6 + 6 + 2 ÷ 7

= 52 ÷ 7

= 7.4

median= 2, 5, 6, 6, 8, 10 , 15

6

median is the middle number from ascending order

mode = 6

mode is the number that occurs the most

range = 15 - 2

13

range is the different between the largest and smallest number

Brainliest is appreciated

Answer:

x=i or no solution exists depending on the user's grade

Step-by-step explanation:

f(x) = 2x^2-5

-7 = 2x^2-5

-2 = 2x^2, x^2=-1, x=i

Answer:

±i = x

Step-by-step explanation:

f(x)=2x^2-5;

f(x)=-7​

-7 = 2x^2 -5

Add 5 to each side

-7+5 = 2x^2 -5+5

-2 =2x^2

Divide by 2

-2/2 =2x^2 /2

-1 = x^2

Take the square root of each side

sqrt(-1) = sqrt(x^2)

±i = x

Answer:

36-x

Step-by-step explanation:

Hi Monica

Answer:

x=10

Step-by-step explanation:

8x-4x-32=8

4x=40

x=10

Answer:

x = 10

Step-by-step explanation:

8x-4(x+8)=8

8x - 4x - 32 = 8

4x - 32 = 8

4x = 40

x = 10

Answer:

1/6 is the fobability of a polygon

Answer:

a positive number

Step-by-step explanation:

-(-) = +

for example, -1 * -1 = 1

Answer:

5 is the answer

Step-by-step explanation:

[tex] \frac{2 z}{y } \\ = \frac{2 \times ( - 5)}{ - 2} \\ = \frac{ - 10}{ - 2} \\ = 5 \: ans.[/tex]

when \(y = -2\) and \(z = -5\), the value of the expression \(2z/y\) is \(5\).

To evaluate the expression \(2z/y\) when \(y = -2\) and \(z = -5\), follow these steps:

1. Substitute the values of \(y\) and \(z\) into the expression:

\(2z/y = 2(-5) / (-2)\)

2. Perform the calculations:

\(2z/y = -10 / (-2) = 5\)

So, when \(y = -2\) and \(z = -5\), the value of the expression \(2z/y\) is \(5\).

Learn more about expression at https://brainly.com/question/723406

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Answer:

8.8 grams

...................

The required 88 Decigrams equals 8.8 grams.

Given that,
To determine 88 Decigrams equals 8.8.

All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.

Fraction is defined as the number of compositions that constitutes the Whole.

here,
10 decigram = 1 gram
88 decigram = 8.8 gram

Thus, the required 88 Decigrams equals 8.8 grams.

Learn more about measurements here:

https://brainly.com/question/4725561

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[tex]\\ \sf\Rrightarrow y-1=\dfrac{2}{3}(x+1)[/tex]

[tex]\\ \sf\Rrightarrow -3-1=\dfrac{2}{3}(a+1)[/tex]

[tex]\\ \sf\Rrightarrow -4=\dfrac{-2(a+1)}{3}[/tex]

[tex]\\ \sf\Rrightarrow -2(a+1)=-4(3)[/tex]

[tex]\\ \sf\Rrightarrow -2(a+1)=-12[/tex]

[tex]\\ \sf\Rrightarrow a+1=\dfrac{-12}{-2}[/tex]

[tex]\\ \sf\Rrightarrow a+1=6[/tex]

[tex]\\ \sf\Rrightarrow a=6-1[/tex]

[tex]\\ \sf\Rrightarrow a=5[/tex]

Answer: An equation with an integer coefficient will NOT always have an integer solution.

Explanation: 3x=25⟹x=253 , therefore it is false.

Hi ;-)

[tex]8x=y \ \ /:8\\\\\boxed{x=\frac{y}{8}}[/tex]

Answer:

see image

Step-by-step explanation:

Answer:

18 ft

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r

113.04 = 2 ( 3.14) * r

113.04 = 6.28 r

Divide each side by 6.28

113.04/6.28 = 6.28r/6.28

18 =r

Answer:

360is  the answer

Step-by-step explanation:

x = number of shaded squares

3x = number of unshaded squares

This is because there are 3 times as many unshaded squares compared to shaded

unshaded = 3*(shaded)

Since there are 5*8 = 40 squares overall, this means,

shaded+unshaded = 40

x+3x = 40

4x = 40

x = 40/4

x = 10

There are 10 shaded squares and 3x = 3*10 = 30 unshaded squares.

So you'll shade in 10 squares in any fashion you prefer.

Answer: f(3) = 14

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given function

f(x) = 4x + 2

Substitute value of the x into the expression

f(3) = 4(3) + 2

Simplify by multiplication

f(3) = 12 + 2

Simplify by addition

f(3) = [tex]\boxed{14}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x + 2z

Step-by-step explanation:

[tex]\frac{15xy+30yz}{15y}[/tex] ← divide each term on the numerator by 15y

= [tex]\frac{15xy}{15y}[/tex] + [tex]\frac{30yz}{15y}[/tex]

= x + 2z

[tex] \frac{4c}{h} - k[/tex]

Step-by-step explanation:

well that is the answer

Answer:

s = (4C/h) - k

Step-by-step explanation:

C = ((s + k)/4)h

multiply by 4/h

4C/h = s + k

subtract k

s = (4C/h) - k

B

Step-by-step explanation:

AM on total = 1/2

so (x+19)/(x+29)=1/2

2x +38 =x + 29

x=-9

Answer:

x = -4

Step-by-step explanation:

[tex]-8x+3=-6x+11\\\\-2x+3=11\\\\-2x=8\\\\x=-4[/tex]

Answer:

x = -4

Step-by-step explanation:

-8x + 3 = -6x + 11

transpose

-8x +6x = 11 - 3

-2x = 8

x = 8/-2

x = -4

Answer:

67

Step-by-step explanation:

Division:-

[tex]\sf\Large\qquad\quad67\\ \begin{array}{cc} \cline{2 - 2}\sf 81 )&\sf \ 5472\\&\sf -487 \downarrow\\ \cline{2-2}& \sf \ \ \ \ 602\\ &\sf \ - 567 \\ \cline{2-2} & \sf \ \035 \\ \cline{2-2} \end{array}\\\\\\ Divisor \rightarrow 81 \\ \\ Quotient \rightarrow 67\\\\Remainder \rightarrow 35[/tex]

Answer:

[69] R [45}

Step-by-step explanation:

dont worry i got it right guys i did this bc i know there is people like me looking for the answer to this!

Answer:

3 hours

Step-by-step explanation:

250 = 50h + 100(4 - h)

250 = 50h + 400 - 100h

250 = -50h + 400

-150 = -50h

h = 3